Question

What is the negative reciprocal $ \dfrac{3}{2} $ ?

Answer 1

Hint: Here we have been given a rational number whose negative reciprocal we have to find. Firstly we know that the reciprocal of a number is done by dividing $ 1 $ by that number which means the numerator and denominator are to be interchanged. Then as we have to find a negative reciprocal we will multiply the obtained value by minus $ 1 $ value and get the desired answer.

Complete step-by-step answer:
The number is given as follows:
 $ \dfrac{3}{2} $ …… $ \left( 1 \right) $
We have to find the negative reciprocal of the above number.
As we know that for any number $ n $ its reciprocal is calculated or defined as $ \dfrac{1}{n} $ using this formula on equation (1) we get the below value,
 $ \Rightarrow \dfrac{1}{\dfrac{3}{2}} $
Now taking the denominator value to the numerator we get,
 $ \Rightarrow \dfrac{2}{3} $
Now as we have to find the negative reciprocal we will multiply the above value by $ -1 $ and simplify it as follows:
 $ \Rightarrow \dfrac{2}{3}\times -1 $
 $ \Rightarrow \dfrac{-2}{3} $
Hence the negative reciprocal of $ \dfrac{3}{2} $ is $ \dfrac{-2}{3} $
So, the correct answer is “ $ \dfrac{-2}{3} $ ”.

Note: Rational numbers are those numbers that can be expressed in the form of $ \dfrac{p}{q} $ where $ q\ne 0 $ .Rational numbers always have repeating or terminating decimal expansion. Real numbers consist of rational numbers as well as irrational numbers where irrational numbers are those which can’t be expressed in the form of $ \dfrac{p}{q} $ . Reciprocal is simply defined as the inverse of a number or value. When we multiply any number by its reciprocal we get the answer as $ 1 $ . Therefore it is also called a multiplicative inverse. We can image it as turning the number upside down where the numerator becomes the denominator and the denominator becomes the numerator.